(This explanation is like a joke ! )

[Introduction]

Since theory of complex functions is a highly developed learning, I have no intention to deny this learning from the stage of its definition. I would just like you to understand that my explanation is also allowable.

[Definition]

Assume a unit circle with center at the origin in a complex plain.

Next, we defines a function as f(x)={a coordinate of a point on the unit circle at the argument x}.

Then, we can express,

=

Therefore,

= | |

= | |

= |

Let = , where is a real number.

then =

So, we are to express this as = .

Note that "" should not be explained as a constant =2.71---, but as a sign.

Thus it can be explained that = -1 means the coordinate of the point at the argument on a unit circle is -1.

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